The relationship between an island's size and the number of species on that island-the island species-area relationship (ISAR)-is one of the most well-known patterns in biogeography and forms the basis for understanding biodiversity loss in response to habitat loss and fragmentation. Nevertheless, there is contention about exactly how to estimate the ISAR and the influence of the three primary ecological mechanisms that drive it - random sampling, disproportionate effects, and heterogeneity. Key to this contention is that estimates of the ISAR are often confounded by sampling and estimates of measures (i.e., island-level species richness) that are not diagnostic of potential mechanisms. Here, we advocate a sampling-explicit approach for disentangling the possible ecological mechanisms underlying the ISAR using parameters derived from individual-based rarefaction curves estimated across spatial scales. If the parameters derived from rarefaction curves at each spatial scale show no relationship with island area, we cannot reject the hypothesis that ISARs result only from random sampling. However, if the derived metrics change with island area, we can reject random sampling as the only operating mechanism and infer that effects beyond sampling (i.e., disproportionate effects and/or heterogeneity) are also operating. Finally, if parameters indicative of within-island spatial variation in species composition (i.e., β-diversity) increase with island area, we can conclude that intra-island compositional heterogeneity plays a role in driving the ISAR. We illustrate this approach using representative case studies, including oceanic islands, natural island-like patches, and habitat fragments from formerly continuous habitat, illustrating several combinations of underlying mechanisms. This approach will offer insight into the role of sampling and other processes that underpin the ISAR, providing a more complete understanding of how, and some indication of why, patterns of biodiversity respond to gradients in island area.